Laurent Stolovitch

Singular complete integrability

We show that a holomorphic vector field in a neighbourhood of its singular point 0∈Cn is analytically normalizable if it has a sufficiently large number of commuting holomorphic vector fields, a sufficiently large number of formal first integrals and that a diophantine small divisors condition related to the linear parts of its centralizer is satisfied.

Progress in normal form theory

In this paper we review recent results about normal forms of systems of analytic differential equations near a fixed point.

Existence of Quasipattern Solutions of the Swift-Hohenberg Equation

We consider the steady Swift–Hohenberg partial differential equation, a one-parameter family of PDEs on the plane that models, for example, Rayleigh–Bénard convection. For values of the parameter near its critical value, we look for small solutions, quasiperiodic in all directions of the plane, and which are invariant under rotations of angle

Complète intégrabilité singulière

{\pi/q, q \geqq 4}

Holomorphic normal form of nonlinear perturbations of nilpotent vector fields

. We solve an unusual small divisor problem and prove the existence of solutions for small parameter values, then address their stability with respect to quasi-periodic perturbations.

Rigidity of Poisson Structures

We are interested in analytic singular Poisson structures with a non zero linear part at the singularity. Using recent work of the author about holomorphic normalization of commutative familly of singular vector fields, we obtain results about normalization of holomorphic Poisson structures.

Bernard Malgrange, 80e anniversaire@@@Bernard Malgrange, 80e anniversaire

We show that an holomorphic vector field in a neighbourhood of its singular point 0 0 ∈ ℂn is analytically normalizable as soon as it has a sufficiently large number of commuting holomorphic vector fields, a sufficiently large number of formal first integrals, and that a Diophantian small divisors condition related to its linear part is satisfied.

NORMAL FORMS OF ANALYTIC PERTURBATIONS OF QUASIHOMOGENEOUS VECTOR FIELDS: RIGIDITY, INVARIANT ANALYTIC SETS AND EXPONENTIALLY SMALL APPROXIMATION

We study a germ of real analytic n-dimensional submanifold of